Thermal conductivity is a property of every material, indicating the extent to which it conducts heat. Heat will always flow from the hot environment to the cold one, in an attempt to equalize the temperature difference. Placing a section of material between a hot and a cold heat sink will control the flow by the test material's inherent thermal resistance. (Thermal resistivity is the inverse of thermal conductivity.) This flow is quantified in terms of a heat flux, q, which is the heat rate, Q, per unit area, A, through which the heat flows in the given direction. In all materials, q is proportional to the temperature difference ΔT and inversely proportional to the thickness, L, according to equation (1):q=−kΔT/L  Equation 1where k is the proportionality factor that varies with temperature for most materials. This relationship, in its generalized form, is defined by Fourier's Law of heat conduction, and k is referred to as thermal conductivity. To determine k as a function of temperature for a particular material, a specimen of the material of known thickness and uniform cross sectional area is subjected to a thermal gradient, and the amount of heat transported is measured by some means. In reality, this process is very complex, due to the need to ensure a unidirectional heat flow (no radial losses or gains along the flow path), and the difficulties in measuring the quantity of heat passing through the specimen.
The thermal conductivity varies nonlinearly with temperature for all materials, therefore it must be measured over the range of use.
Thermal conductivity is an intrinsic property of each material. It can range from several thousand W/(m·K) (diamond) to five decades lower (aerogel). Because of this enormous range, there is no single method of measurement that can be used for all. While there is no strict division based on thermal conductivity, it is common practice to refer to a material as being of high conductivity with k>40 W/(m·K), medium conductivity 2<k<40 W/(m·K) and low conductivity 0.1<k<2 W/(m·K). Below 0.1 W/(m·K) they are called insulators. The Guarded Heat Flow Meter is most useful for testing medium and low conductivity materials. It is not appropriate for either high conductivity materials or insulators.
A commonly employed configuration described in literature and used in commercially available instruments is depicted in FIG. 1. It consists of a stack of layers S, where the unknown 1U is sandwiched between a heater plate 2H and a heat sink 3S. To avoid having to drill or groove into the unknown test specimen, for placing in temperature sensors, like thermocouples, in some cases, a layer 4 of very high conductivity material, such as copper, silver or aluminum, is interposed with suitable cavities, C, for said temperature sensors 5T (FIG. 1). The heater plate 2H contains a heat source 6H, which is most often an electrically heated resistance wire. The use of other means, such as thermoelectric heaters, circulated steam and radiation sources have been also described.
For equation 1 to apply, only the heat flow along the axis of stack S must be considered. Since heat will propagate in all directions along temperature gradients that exist, methods have been implemented and codified, such as described in ASTM E1530-19, to deal with minimizing the effects of these extraneous heat paths. In this “Standard Test Method for Evaluating the Resistance to Thermal Transmission of Materials by the Guarded Heat Flow Meter Technique”, a dimensionally defined and of well characterized thermal conductivity piece 7 is placed in series with the unknown specimen, 1U, in the path of the axial heat flow (Q1). In principle, temperature sensors could be placed directly into this section at well defined intervals, to determine the temperature gradient along it, but in practice, using heat spreader plate 4 is more common. Applying Equation 1 to this section, the heat flow Q1 will be defined from ΔTR=T4−T3, having all other terms known. FIG. 3 shows temperatures with an arrow such as T3, T4. FIG. 4 labels item 3050 as the pressure generator. Using the thusly determined Q1, when substituted back in Equation 1 for the unknown specimen 1U and using ΔT=T2-T1, will yield its thermal conductivity, as long as Q1 is constant while passing through the stack. In reality, it will not be so, as its environment is at different temperatures (T4>T3>T2>T1) along its axis. Theoretically, if one places a guard cylinder 8G around the stack and produces an axial gradient along this cylinder exactly matching that of the stack, radial losses/gains (Q4, Q5, Q6) would be zero. However, this is nearly impossible, so a compromise is commonly used where the guard is kept at some mean temperature of the unknown, the metering section, or the combination of the two, to minimize and balance parasitic radial heat flow (Q4, Q5, etc.). A novel part of the invention addresses this issue. Furthermore, calibration procedures are also used, using well characterized reference species and defined testing protocols, to quantify the combined losses. It is imperative that calibration protocols be identical to testing protocols, including clamping pressures, guard positioning and guard temperatures.
Unavoidable barriers in the path of heat flow are thermal interfaces. They produce thermal interface resistances on either sides of the unknown specimen 1U and of the reference section. These are kept as constant as possible by the application of thermal grease or other similar means, FIG. 3 210,211.
The components of the stack S are compressed together usually with pneumatic cylinders, or fully compressed springs.
The final component in the stack S is the heat sink 3S, usually cooled with tap water or refrigerated water, circulated through cooling coils or channels. In some instances, thermoelectric coolers were used successfully. In nearly all cases, however, this type of heat sink becomes a limiting factor in realizing higher temperatures.
Thermal conductivity of most materials varies with temperature. In order to assign a single number to any discrete temperature, it is necessary to measure it in a temperature range straddling the discrete point. It is physically impossible to measure thermal conductivity with this range being zero, as there is a need to establish a finite and reliably measurable thermal gradient. However, the wider this gradient, the further the calculated value based on the measurement will deviate from the true value. As a practical matter, ranges of 10 C to 30 C are used. This necessitates having the heat sink 3S at a high temperature when high temperature measurements are being made. In form of example, an upper heater block 6H temperature of 300 C necessitates a heat sink 3S temperature of at least 270 C. This is not possible to achieve with water cooled heat sinks, as water will boil at 100 C. So, current instruments employing the method, have been equipped with a removable spacer made of low conductance material which is switched out for the low end region, T<80 C, and then installed for temperatures above. This necessity virtually denied the possibility of an uninterrupted and continuous test protocol, to cover sub ambient to well elevated (up to and above 100 C heater), employing 30 C total heater to heat sink temperature differences. The present invention eliminates the need for such a spacer, by virtue of allowing the heat sink to float up to the desired temperature, not far below the heater, and thus affording a single uninterrupted test protocol for a wide range of temperatures.
To compress the stack and the unknown, most commonly, a pneumatic cylinder is used, fed from an adjustable pressure regulator. While this is straightforward, its limitations are many. Pneumatic cylinders have a certain drag from the seals, so they tend not to move until air pressure builds up and, therefore, the adjustment is very coarse. This is detrimental, especially at low pressures, when used for deformable specimens.
The other commonly employed means is a simple spring that is compressed with a suitable lever until it locks. This method works well for specimens of the same thickness, but will usually vary the compressive force for varied specimen thicknesses.
The present invention remedies many of the above detailed problems associated with this measurement technique, and it also provides a path to extend the measurement capabilities to include modulated and programmed pressures to be included in testing protocols.